API Calls with multiple indexes

Yes, that would most likely help with the API requests.

If you’re fine with Autocomplete suggestions being all grouped together, then the “All Posts” option should be fine for that. Clicking individual post types in that settings page also creates separate indexes for each, meaning there’s more to configure or perhaps re-configure to match. So there’s definitely benefit to just “All Posts” to match up with having searchable posts enabled.

Does the plugin support this multi-index search at all?
https://www.algolia.com/doc/guides/building-search-ui/ui-and-ux-patterns/multi-index-search/ios/

Out of box with our default templates, no, but they can be customized as needed with the information at https://www.algolia.com/doc/guides/building-search-ui/ui-and-ux-patterns/multi-index-search/js/

Note that I linked to the instantsearch.js version of the docs, and not the iOS/Swift version.

Information about template customization can be found at https://github.com/WebDevStudios/wp-search-with-algolia/wiki/Customize-Templates